Four persons a b c and d went to a hotel to take tiffin the total bill was rupees 60 agreed to pay half the sum of the amounts paid by the other three agree to pay one third of the sum of the amount paid by the other three and see you agree to pay one fourth of the sum of the amount paid by the other three how much did d pay
Answers
Answer:
13
Step-by-step explanation:
Let A, B, C, D pays x₁, x₂, x₃, x₄ Rupees respectively.
We have, x₁ + x₂ + x₃ + x₄ = 60 ---- [1]
A agrees to pay half of the sum of money paid by the other three.
So, x₁ = 1/2 ( x₂ + x₃ + x₄)
=> 2x₁ = x₂ + x₃ + x₄ -------------- [2]
We can solve for x₁
substitute [2] in [1]
x₁ + x₂ + x₃ + x₄ = 60
x₁ + 2x₁ = 60
3x₁ = 60
x₁ = 20.
B agrees to pay one third of the sum of money paid by other three.
x₂ = 1/3 ( x₁ + x₃ + x₄)
3x₂ = x₁ + x₃ + x₄ -------------------- [3]
We can solve for x₂,
substitute [3] in [1]
x₁ + x₂ + x₃ + x₄ = 60
3x₂ + x₂ = 60
4x₂ = 60
=> x₂ = 15.
C agrees to pay one fourth of the sum of money paid by the other three,
x₃ = 1/4 ( x₁ + x₂ + x₄)
4x₃ = x₁ + x₂ + x₄ -------------- [4]
We can solve for x₃,
substitute [4] in [1]
x₁ + x₂ + x₃ + x₄ = 60
4x₃ + x₃ = 60
5x₃ = 60
=> x₃ = 12
Substitute value of x₁, x₂ and x₃ in [1]
x₁ + x₂ + x₃ + x₄ = 60
20 + 15 + 12 + x₄ = 60
47 + x₄ = 60
x₄ = 13
Therefore, Person D pays 13 Rupees.